Regular and irregular polygons
Distinguish between regular and irregular polygons based on reasoning about equal sides and equal angles
Lesson
Set out your lesson
“Regular and irregular polygons means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Paper shapes or a ruler and pencil
- Shape name cards
Extra for the adult
Worked example. A rectangle has four right angles. Naming the property is the check.
Optional challenge. For Regular and irregular polygons, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Regular and irregular polygons, not mastery.
Share and support
Family records and proof options
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Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.
Practice this concept
Start practiceRegular and irregular polygons practice
Practice key ideas from Regular and irregular polygons.
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
Illustrative Mathematics · Practice link — not the full lesson
Always, Sometimes, Never
Before you open · source notes
Always/sometimes/never statements support classifying regular and irregular polygons. Not every circle theorem.
Free, no sign-in. A teacher solution is on the same page, so use the student view with your child.
Before you openAsk the learner to judge a polygon statement as always, sometimes, or never and give an example.
Opening this link does not save learning or assess mastery.
Source, access and review notes
Public Illustrative Mathematics task page. The .html address responds HTTP 308 to this URL. An anonymous GET of this URL on 2026-11-12 returned HTTP 200 with no login or payment prompt. Where a teacher solution is present, it is on the same page as the student task; this check did not find a separate locked student view. An adult can use the student view section and should not read a solution aloud. Advertising was not observed in the fetched HTML text; that is not a browser, device, or ad-free guarantee. This is a paper or discussion task, not an automatically marked interactive game. Opening the link does not save practice or assess mastery. Diagrams on the page use missing or filename-only alt text, so they are not an accessible image equivalent. Accessibility still depends on an adult describing the picture.
Illustrative Mathematics. “Always, Sometimes, Never.” Licensed CC BY-NC-SA 4.0. External task; Gakuva does not copy, host, embed, or redistribute it.
CC BY-NC-SA 4.0 — link only
Check understanding
- Classify a set of polygons as regular or irregular
- Explain that a regular pentagon has 5 equal sides and 5 equal angles
- Identify that a rectangle is irregular (equal angles but not all equal sides) unless it is a square
“If you show your child a stop sign (regular octagon) and a wonky eight-sided shape, can they explain which is regular and which is irregular — and why?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Geometry
- Age range
- Ages 9–12
Standards